In this study the cyclic linear random process is defined, that combines the properties of linear random process and cyclic random process. This expands the possibility describing cyclic signals and processes within the framework of linear random processes theory and generalizes their known mathematical model as a linear periodic random process. The conditions for the kernel are given and the probabilistic characteristics of generated process of linear random process in order to be a cyclic random process. The advantages of the cyclic linear random process are presented. It can be used as the mathematical model of the cyclic stochastic signals and processes in various fields of science and technology.
Serhii Lupenko, Nadiia Lutsyk, Oleh Yasniy and Łukasz Sobaszek
The new methods of statistical analysis of heart rhythm were developed based on its generalized mathematical model in a form of random rhythm function, that allows to increase the informativeness and detailed analysis of heart rhythm in cardiovascular information systems. Three information criteria (BIC, AIC and AICc) were used to determine the cumulative distribution functions that best describe the sample and to assess the unknown parameters of distributions. The usage of the rhythm function to analyse heart rhythm allows to consider much better its time structure that is the basis to improve the accuracy of diagnosis of cardiac rhythm.